Question: Expand and combine like terms. $(4d^2-2d^7)^2=$
We can expand this expression using the "perfect square" pattern (where $P$ and $Q$ can be any monomial): $(P+Q)^2=P^2+2PQ+Q^2$ Since we have a minus sign, let's rewrite the binomial as a sum where the second term is negative, then use the pattern. $\begin{aligned} &\phantom{=}\left(4d^2-2d^7\right)^2 \\\\ &=\left(4d^2+\left(-2d^7\right)\right)^2 \\\\ &=(4d^2)^2+2(4d^2)(-2d^7)+(-2d^7)^2 \\\\ &=16d^4-16d^9+4d^{14} \\\\ &=4d^{14}-16d^9+16d^4 \end{aligned}$